R Notebook

library(relaimpo)

Loading required package: MASS
package ‘MASS’ was built under R version 3.6.2
Attaching package: ‘MASS’

The following object is masked from ‘package:dplyr’:

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Loading required package: boot
Loading required package: survey
package ‘survey’ was built under R version 3.6.2Loading required package: grid
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Attaching package: ‘Matrix’

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Loading required package: survival

Attaching package: ‘survival’

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Attaching package: ‘survey’

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Loading required package: mitools
This is the global version of package relaimpo.

If you are a non-US user, a version with the interesting additional metric pmvd is available

from Ulrike Groempings web site at prof.beuth-hochschule.de/groemping.

house_price <- read_csv(here("data/kc_house_data.csv"))

glimpse(house_price)

house_price <- house_price %>%
  select(-c(date, id, sqft_living15, sqft_lot15, zipcode))

summary(house_price)

     price            bedrooms        bathrooms      sqft_living   
 Min.   :  75000   Min.   : 0.000   Min.   :0.000   Min.   :  290  
 1st Qu.: 321950   1st Qu.: 3.000   1st Qu.:1.750   1st Qu.: 1427  
 Median : 450000   Median : 3.000   Median :2.250   Median : 1910  
 Mean   : 540088   Mean   : 3.371   Mean   :2.115   Mean   : 2080  
 3rd Qu.: 645000   3rd Qu.: 4.000   3rd Qu.:2.500   3rd Qu.: 2550  
 Max.   :7700000   Max.   :33.000   Max.   :8.000   Max.   :13540  
    sqft_lot           floors      waterfront           view       
 Min.   :    520   Min.   :1.000   Mode :logical   Min.   :0.0000  
 1st Qu.:   5040   1st Qu.:1.000   FALSE:21450     1st Qu.:0.0000  
 Median :   7618   Median :1.500   TRUE :163       Median :0.0000  
 Mean   :  15107   Mean   :1.494                   Mean   :0.2343  
 3rd Qu.:  10688   3rd Qu.:2.000                   3rd Qu.:0.0000  
 Max.   :1651359   Max.   :3.500                   Max.   :4.0000  
   condition         grade          sqft_above   sqft_basement       yr_built   
 Min.   :1.000   Min.   : 1.000   Min.   : 290   Min.   :   0.0   Min.   :1900  
 1st Qu.:3.000   1st Qu.: 7.000   1st Qu.:1190   1st Qu.:   0.0   1st Qu.:1951  
 Median :3.000   Median : 7.000   Median :1560   Median :   0.0   Median :1975  
 Mean   :3.409   Mean   : 7.657   Mean   :1788   Mean   : 291.5   Mean   :1971  
 3rd Qu.:4.000   3rd Qu.: 8.000   3rd Qu.:2210   3rd Qu.: 560.0   3rd Qu.:1997  
 Max.   :5.000   Max.   :13.000   Max.   :9410   Max.   :4820.0   Max.   :2015  
  yr_renovated         lat             long       
 Min.   :   0.0   Min.   :47.16   Min.   :-122.5  
 1st Qu.:   0.0   1st Qu.:47.47   1st Qu.:-122.3  
 Median :   0.0   Median :47.57   Median :-122.2  
 Mean   :  84.4   Mean   :47.56   Mean   :-122.2  
 3rd Qu.:   0.0   3rd Qu.:47.68   3rd Qu.:-122.1  
 Max.   :2015.0   Max.   :47.78   Max.   :-121.3  

We should convert the waterfront to a logical vector and try it as a categorical variable.

house_price <- house_price %>%
  mutate_at("waterfront", as.logical)

house_price <- house_price %>%
  mutate(renovated = ifelse(yr_renovated == 0, FALSE, TRUE)) %>%
  select(-yr_renovated)

unique(house_price$condition)

[1] 3 5 4 1 2

unique(house_price$grade)

 [1]  7  6  8 11  9  5 10 12  4  3 13  1

Grade is a clasification of the house acording to the material that they use for building the house, so when the building has a greater grade the cost per unit measure is higher. In this sense we can consider this as categorical ordinal because they imply a order but it isn’t a numerical interval order. We can say the same about condition.

house_price <- house_price%>%
  mutate_at("condition", as.factor) %>%
  mutate_at("grade", as.factor)

mod_pre <- lm(price ~ ., data = house_price)

alias(mod_pre)

Model :
price ~ bedrooms + bathrooms + sqft_living + sqft_lot + floors + 
    waterfront + view + condition + grade + sqft_above + sqft_basement + 
    yr_built + lat + long + renovated

Complete :
              (Intercept) bedrooms bathrooms sqft_living sqft_lot floors
sqft_basement  0           0        0         1           0        0    
              waterfrontTRUE view condition2 condition3 condition4 condition5
sqft_basement  0              0    0          0          0          0        
              grade3 grade4 grade5 grade6 grade7 grade8 grade9 grade10 grade11
sqft_basement  0      0      0      0      0      0      0      0       0     
              grade12 grade13 sqft_above yr_built lat long renovatedTRUE
sqft_basement  0       0      -1          0        0   0    0           

Nonzero entries in the “complete” matrix show that those terms are linearly dependent on UseMonthly. This means they’re highly correlated, but terms can be highly correlated without being linearly dependent.

So I will drop sqft_basement, sqft_living, sqft_above because the suppose to have a linearly dependent, if I interpreted in good way the mean.

house_price <- house_price %>%
  select(-c(sqft_basement, sqft_living, sqft_above))

house_price_no_numetic <- house_price %>%
  select_if(!is.numeric)

Error in !is.numeric : invalid argument type

house_price_numeric %>%
  ggpairs()

NA
NA
NA
NA
NA

house_price_no_numetic %>%
  ggpairs()

summary(model_price_bath)

Call:
lm(formula = price ~ bathrooms, data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1438157  -184525   -41525   113220  5925322 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    10708       6211   1.724   0.0847 .  
bathrooms     250326       2760  90.714   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 312400 on 21611 degrees of freedom
Multiple R-squared:  0.2758,    Adjusted R-squared:  0.2757 
F-statistic:  8229 on 1 and 21611 DF,  p-value: < 2.2e-16

The bathroom only explain the price in a 27.57 %

par(mfrow = c(2,2))
plot(model_price_bath)

The scale location plot follow a trend to go up and the normal plot the residuals aren’t normal at the end

house_price %>%
  add_residuals(model_price_bath) %>%
  select_if(function(x) is.numeric(x)) %>%
  select(-c(price, bathrooms)) %>%
  ggpairs()

The view is high correlative with the residual let’s check it in combination with bathroom

model_price_bath_view <- lm(price ~ bathrooms + view, data = house_price) 

summary(model_price_bath_view)

Call:
lm(formula = price ~ bathrooms + view, data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1254186  -169132   -34786   113486  5729504 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    34550       5816    5.94 2.89e-09 ***
bathrooms     222618       2624   84.84  < 2e-16 ***
view          148332       2637   56.25  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 291800 on 21610 degrees of freedom
Multiple R-squared:  0.3683,    Adjusted R-squared:  0.3682 
F-statistic:  6298 on 2 and 21610 DF,  p-value: < 2.2e-16

The combination of the bathrooms and view could explain in a 36% the price

par(mfrow = c(2,2))
plot(model_price_bath_view)

The residual continue to have a trend and they aren’t normal at the end.

Now let’s try to find a feature inside our categorical data

house_price %>%
  add_residuals(model_price_bath_view) %>%
  select(waterfront, condition, grade, renovated, resid) %>%
  ggpairs()

NA

The condition looks quite interesting special around 3

summary(model_bath_view_condition)

Call:
lm(formula = price ~ bathrooms + view + condition, data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1267263  -169667   -32811   113469  5740221 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    22246      53084   0.419    0.675    
bathrooms     228574       2672  85.544   <2e-16 ***
view          145369       2631  55.248   <2e-16 ***
condition2    -37180      57440  -0.647    0.517    
condition3    -19290      53128  -0.363    0.717    
condition4     26272      53170   0.494    0.621    
condition5     80272      53508   1.500    0.134    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 290300 on 21606 degrees of freedom
Multiple R-squared:  0.3751,    Adjusted R-squared:  0.3749 
F-statistic:  2161 on 6 and 21606 DF,  p-value: < 2.2e-16

To be honest the increase is only in 1 %. Let’s check the anova

anova(model_price_bath_view, model_bath_view_condition)

Analysis of Variance Table

Model 1: price ~ bathrooms + view
Model 2: price ~ bathrooms + view + condition
  Res.Df        RSS Df  Sum of Sq      F    Pr(>F)    
1  21610 1.8402e+15                                   
2  21606 1.8204e+15  4 1.9854e+13 58.912 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The model include condition is better because the p values is lower than 0.005 but we can add other more no categorical variable and see wath hapen before add condition

house_price %>%
  add_residuals(model_price_bath_view) %>%
  select_if(function(x) is.numeric(x)) %>%
  select(-c(price, bathrooms, view)) %>%
  ggpairs()

Lat continue to be high correlative with resid so lets include it

model_bath_view_lat <- lm(price ~ bathrooms + view + lat, 
                          data = house_price)

summary(model_bath_view_lat)

Call:
lm(formula = price ~ bathrooms + view + lat, data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1261035  -137379   -29702    89832  5667993 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -36980261     633204  -58.40   <2e-16 ***
bathrooms      219219       2439   89.88   <2e-16 ***
view           148107       2451   60.44   <2e-16 ***
lat            778428      13316   58.46   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 271200 on 21609 degrees of freedom
Multiple R-squared:  0.4545,    Adjusted R-squared:  0.4544 
F-statistic:  6002 on 3 and 21609 DF,  p-value: < 2.2e-16

With lat the r^2 going up more than 10. Let’s check the graphs

par(mfrow = c(2,2))
plot(model_bath_view_lat)

The result continue to be quite the same

model_bath_view_lat_1 <- lm(log(price) ~ bathrooms + view + lat, 
                          data = house_price)

summary(model_bath_view_lat_1)

Call:
lm(formula = log(price) ~ bathrooms + view + lat, data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.85904 -0.22650 -0.01743  0.21097  1.91082 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -66.436541   0.821213  -80.90   <2e-16 ***
bathrooms     0.337090   0.003163  106.56   <2e-16 ***
view          0.172717   0.003178   54.34   <2e-16 ***
lat           1.655402   0.017270   95.86   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3517 on 21609 degrees of freedom
Multiple R-squared:  0.5542,    Adjusted R-squared:  0.5541 
F-statistic:  8955 on 3 and 21609 DF,  p-value: < 2.2e-16

par(mfrow = c(2,2))
plot(model_bath_view_lat_1)

Even with a log in price the residual continu to follow a trend, nut the data looks more normal Let’s add a categorical variable to end

house_price %>%
  add_residuals(model_bath_view_lat_1) %>%
  select(waterfront, condition, grade, renovated, resid) %>%
  ggpairs()

Actually grade looks a great option let’s take it

model_bath_view_lat_grade <- lm(log(price) ~ bathrooms + view + lat + grade, 
                          data = house_price)

summary(model_bath_view_lat_grade)

Call:
lm(formula = log(price) ~ bathrooms + view + lat + grade, data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.58146 -0.18860 -0.01772  0.17675  1.31907 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -58.326621   0.754921 -77.262  < 2e-16 ***
bathrooms     0.124511   0.003531  35.267  < 2e-16 ***
view          0.125495   0.002726  46.038  < 2e-16 ***
lat           1.476731   0.014620 101.005  < 2e-16 ***
grade3        0.476419   0.340584   1.399  0.16188    
grade4        0.237571   0.300003   0.792  0.42843    
grade5        0.350229   0.295579   1.185  0.23607    
grade6        0.510331   0.295049   1.730  0.08371 .  
grade7        0.699234   0.295031   2.370  0.01780 *  
grade8        0.897297   0.295086   3.041  0.00236 ** 
grade9        1.171552   0.295153   3.969 7.23e-05 ***
grade10       1.393909   0.295271   4.721 2.36e-06 ***
grade11       1.600347   0.295586   5.414 6.22e-08 ***
grade12       1.847965   0.296942   6.223 4.96e-10 ***
grade13       2.145218   0.306648   6.996 2.72e-12 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2949 on 21598 degrees of freedom
Multiple R-squared:  0.6866,    Adjusted R-squared:  0.6864 
F-statistic:  3380 on 14 and 21598 DF,  p-value: < 2.2e-16

Grade is a very good choose the problem is that the p error is more that 0.05 in grade 3,4,5. Let’s check anova

anova(model_bath_view_lat_1, model_bath_view_lat_grade)

Analysis of Variance Table

Model 1: log(price) ~ bathrooms + view + lat
Model 2: log(price) ~ bathrooms + view + lat + grade
  Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
1  21609 2672.6                                  
2  21598 1878.8 11    793.73 829.48 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

For sure the model with grade is much better so we should include it, even with the high P error in the 3 variables, because the p error in anova is lower than 0.05 and the r^2 improve a lot with it so let’s check the residuals plots

par(mfrow = c(2,2))
plot(model_bath_view_lat_grade)

not plotting observations with leverage one:
  19453

It is’t significally better the trend of the residual is less and they look a litle more normal, but no 100% better. 0.6864

model_final_1 <- lm(log(price) ~ bathrooms + view + lat + grade + bathrooms:view, 
                          data = house_price)

summary(model_final_1)

Call:
lm(formula = log(price) ~ bathrooms + view + lat + grade + bathrooms:view, 
    data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.57636 -0.18872 -0.01809  0.17704  1.35638 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -58.426449   0.754702 -77.417  < 2e-16 ***
bathrooms        0.129974   0.003680  35.322  < 2e-16 ***
view             0.163892   0.007829  20.933  < 2e-16 ***
lat              1.478831   0.014617 101.172  < 2e-16 ***
grade3           0.475465   0.340377   1.397  0.16246    
grade4           0.229094   0.299824   0.764  0.44482    
grade5           0.340950   0.295404   1.154  0.24844    
grade6           0.501788   0.294873   1.702  0.08882 .  
grade7           0.688239   0.294859   2.334  0.01960 *  
grade8           0.883633   0.294918   2.996  0.00274 ** 
grade9           1.158244   0.294984   3.926 8.65e-05 ***
grade10          1.382626   0.295099   4.685 2.81e-06 ***
grade11          1.596951   0.295407   5.406 6.52e-08 ***
grade12          1.865077   0.296779   6.284 3.35e-10 ***
grade13          2.210788   0.306717   7.208 5.87e-13 ***
bathrooms:view  -0.015061   0.002879  -5.231 1.70e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2948 on 21597 degrees of freedom
Multiple R-squared:  0.687, Adjusted R-squared:  0.6868 
F-statistic:  3160 on 15 and 21597 DF,  p-value: < 2.2e-16

model_final_2 <- lm(log(price) ~ bathrooms + view + lat + grade + bathrooms:lat, 
                          data = house_price)

summary(model_final_2)

Call:
lm(formula = log(price) ~ bathrooms + view + lat + grade + bathrooms:lat, 
    data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.59676 -0.18863 -0.01769  0.17679  1.33299 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -67.465572   2.237132 -30.157  < 2e-16 ***
bathrooms       4.546040   1.018923   4.462 8.18e-06 ***
view            0.125564   0.002725  46.081  < 2e-16 ***
lat             1.669005   0.046656  35.772  < 2e-16 ***
grade3          0.505613   0.340510   1.485  0.13759    
grade4          0.237212   0.299879   0.791  0.42894    
grade5          0.348150   0.295457   1.178  0.23867    
grade6          0.504813   0.294930   1.712  0.08698 .  
grade7          0.690046   0.294917   2.340  0.01930 *  
grade8          0.887993   0.294972   3.010  0.00261 ** 
grade9          1.163208   0.295038   3.943 8.09e-05 ***
grade10         1.386170   0.295155   4.696 2.66e-06 ***
grade11         1.594354   0.295467   5.396 6.88e-08 ***
grade12         1.842987   0.296821   6.209 5.43e-10 ***
grade13         2.155239   0.306530   7.031 2.11e-12 ***
bathrooms:lat  -0.092936   0.021417  -4.339 1.43e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2948 on 21597 degrees of freedom
Multiple R-squared:  0.6869,    Adjusted R-squared:  0.6867 
F-statistic:  3158 on 15 and 21597 DF,  p-value: < 2.2e-16

model_final_3 <- lm(log(price) ~ bathrooms + view + lat + grade + bathrooms:grade, 
                          data = house_price)

summary(model_final_3)

Call:
lm(formula = log(price) ~ bathrooms + view + lat + grade + bathrooms:grade, 
    data = house_price)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.5886 -0.1879 -0.0178  0.1782  1.2944 

Coefficients: (1 not defined because of singularities)
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)       -5.820e+01  7.544e-01 -77.145  < 2e-16 ***
bathrooms          1.403e-01  5.241e-02   2.677 0.007442 ** 
view               1.249e-01  2.724e-03  45.847  < 2e-16 ***
lat                1.474e+00  1.461e-02 100.862  < 2e-16 ***
grade3             2.165e-01  3.605e-01   0.601 0.548098    
grade4             9.442e-02  3.872e-01   0.244 0.807357    
grade5             2.508e-01  3.015e-01   0.832 0.405361    
grade6             4.118e-01  2.950e-01   1.396 0.162777    
grade7             7.160e-01  2.945e-01   2.431 0.015056 *  
grade8             9.759e-01  2.948e-01   3.310 0.000934 ***
grade9             1.130e+00  2.960e-01   3.819 0.000134 ***
grade10            1.158e+00  2.973e-01   3.893 9.92e-05 ***
grade11            1.454e+00  3.017e-01   4.820 1.45e-06 ***
grade12            1.956e+00  3.147e-01   6.215 5.22e-10 ***
grade13            2.066e+00  4.057e-01   5.093 3.55e-07 ***
bathrooms:grade3   1.022e+00  4.835e-01   2.113 0.034588 *  
bathrooms:grade4   1.424e-01  2.764e-01   0.515 0.606481    
bathrooms:grade5   7.346e-02  7.671e-02   0.958 0.338267    
bathrooms:grade6   6.351e-02  5.460e-02   1.163 0.244790    
bathrooms:grade7  -2.486e-02  5.266e-02  -0.472 0.636786    
bathrooms:grade8  -4.915e-02  5.290e-02  -0.929 0.352825    
bathrooms:grade9  -1.662e-04  5.365e-02  -0.003 0.997528    
bathrooms:grade10  6.303e-02  5.416e-02   1.164 0.244479    
bathrooms:grade11  2.627e-02  5.554e-02   0.473 0.636241    
bathrooms:grade12 -4.255e-02  5.887e-02  -0.723 0.469881    
bathrooms:grade13         NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2943 on 21588 degrees of freedom
Multiple R-squared:  0.6881,    Adjusted R-squared:  0.6877 
F-statistic:  1984 on 24 and 21588 DF,  p-value: < 2.2e-16

Iteration between bathrooms and view and with lat only increase R by 0.2% more

model_final_4 <- lm(log(price) ~ bathrooms + view + lat + grade + view:lat, 
                          data = house_price)

summary(model_final_4)

Call:
lm(formula = log(price) ~ bathrooms + view + lat + grade + view:lat, 
    data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.58237 -0.18897 -0.01757  0.17703  1.32343 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -58.614435   0.777143 -75.423  < 2e-16 ***
bathrooms     0.124605   0.003531  35.289  < 2e-16 ***
view          1.688361   1.002498   1.684  0.09217 .  
lat           1.482786   0.015127  98.022  < 2e-16 ***
grade3        0.477584   0.340574   1.402  0.16084    
grade4        0.237804   0.299993   0.793  0.42796    
grade5        0.349944   0.295569   1.184  0.23644    
grade6        0.509979   0.295039   1.729  0.08391 .  
grade7        0.698816   0.295022   2.369  0.01786 *  
grade8        0.896920   0.295076   3.040  0.00237 ** 
grade9        1.171142   0.295144   3.968 7.27e-05 ***
grade10       1.393703   0.295262   4.720 2.37e-06 ***
grade11       1.600690   0.295576   5.415 6.18e-08 ***
grade12       1.848950   0.296932   6.227 4.85e-10 ***
grade13       2.150237   0.306655   7.012 2.42e-12 ***
view:lat     -0.032860   0.021078  -1.559  0.11902    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2949 on 21597 degrees of freedom
Multiple R-squared:  0.6866,    Adjusted R-squared:  0.6864 
F-statistic:  3155 on 15 and 21597 DF,  p-value: < 2.2e-16

model_final_5 <- lm(log(price) ~ bathrooms + view + lat + grade + view:grade, 
                          data = house_price)

summary(model_final_5)

Call:
lm(formula = log(price) ~ bathrooms + view + lat + grade + view:grade, 
    data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.57978 -0.18848 -0.01764  0.17700  1.33238 

Coefficients: (2 not defined because of singularities)
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -58.381327   0.753768 -77.453  < 2e-16 ***
bathrooms      0.125520   0.003528  35.579  < 2e-16 ***
view           0.009631   0.050762   0.190  0.84952    
lat            1.477882   0.014599 101.232  < 2e-16 ***
grade3         0.476393   0.339949   1.401  0.16112    
grade4         0.212357   0.299948   0.708  0.47897    
grade5         0.339713   0.295056   1.151  0.24960    
grade6         0.504568   0.294501   1.713  0.08667 .  
grade7         0.696312   0.294482   2.365  0.01806 *  
grade8         0.890497   0.294538   3.023  0.00250 ** 
grade9         1.181441   0.294610   4.010 6.09e-05 ***
grade10        1.391084   0.294751   4.720 2.38e-06 ***
grade11        1.612001   0.295216   5.460 4.80e-08 ***
grade12        1.976621   0.297819   6.637 3.28e-11 ***
grade13        2.353857   0.319852   7.359 1.92e-13 ***
view:grade3          NA         NA      NA       NA    
view:grade4    0.292343   0.135960   2.150  0.03155 *  
view:grade5    0.184996   0.059117   3.129  0.00175 ** 
view:grade6    0.164451   0.052497   3.133  0.00174 ** 
view:grade7    0.126383   0.051165   2.470  0.01351 *  
view:grade8    0.133667   0.051002   2.621  0.00878 ** 
view:grade9    0.086454   0.051075   1.693  0.09053 .  
view:grade10   0.115438   0.051245   2.253  0.02429 *  
view:grade11   0.101042   0.051819   1.950  0.05120 .  
view:grade12   0.034031   0.053944   0.631  0.52814    
view:grade13         NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2944 on 21589 degrees of freedom
Multiple R-squared:  0.6879,    Adjusted R-squared:  0.6876 
F-statistic:  2069 on 23 and 21589 DF,  p-value: < 2.2e-16

model_final_6 <- lm(log(price) ~ bathrooms + view + lat + grade + lat:grade, 
                          data = house_price)

summary(model_final_6)

Call:
lm(formula = log(price) ~ bathrooms + view + lat + grade + lat:grade, 
    data = house_price)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.59526 -0.18978 -0.01655  0.17638  1.33769 

Coefficients: (1 not defined because of singularities)
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.948e+01  5.970e+01   1.164   0.2445    
bathrooms    1.253e-01  3.534e-03  35.444  < 2e-16 ***
view         1.257e-01  2.726e-03  46.113  < 2e-16 ***
lat         -1.212e+00  1.256e+00  -0.965   0.3345    
grade3      -1.472e+02  8.258e+01  -1.783   0.0746 .  
grade4      -9.544e+01  6.474e+01  -1.474   0.1405    
grade5      -1.124e+02  6.015e+01  -1.869   0.0616 .  
grade6      -1.277e+02  5.975e+01  -2.138   0.0325 *  
grade7      -1.309e+02  5.971e+01  -2.192   0.0284 *  
grade8      -1.220e+02  5.971e+01  -2.044   0.0410 *  
grade9      -1.258e+02  5.974e+01  -2.107   0.0352 *  
grade10     -1.245e+02  5.984e+01  -2.080   0.0375 *  
grade11     -1.076e+02  6.026e+01  -1.786   0.0741 .  
grade12     -1.194e+02  6.251e+01  -1.911   0.0560 .  
grade13      2.419e+00  3.327e-01   7.273 3.65e-13 ***
lat:grade3   3.109e+00  1.741e+00   1.786   0.0741 .  
lat:grade4   2.012e+00  1.362e+00   1.477   0.1396    
lat:grade5   2.372e+00  1.265e+00   1.875   0.0609 .  
lat:grade6   2.698e+00  1.257e+00   2.146   0.0319 *  
lat:grade7   2.768e+00  1.256e+00   2.204   0.0275 *  
lat:grade8   2.587e+00  1.256e+00   2.059   0.0395 *  
lat:grade9   2.672e+00  1.257e+00   2.126   0.0335 *  
lat:grade10  2.648e+00  1.259e+00   2.104   0.0354 *  
lat:grade11  2.299e+00  1.268e+00   1.813   0.0698 .  
lat:grade12  2.552e+00  1.315e+00   1.941   0.0523 .  
lat:grade13         NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2947 on 21588 degrees of freedom
Multiple R-squared:  0.6872,    Adjusted R-squared:  0.6869 
F-statistic:  1977 on 24 and 21588 DF,  p-value: < 2.2e-16

0.6864 f1 = 0.6868 p error < 0.05 f2 = 0.6867 p error < 0.05 f3 = 0.6877 rr P error > 0.05 most of the time f4 = 0.6864 p error > 0.05 f5 = 0.6876 p error > 0.05 in 6 cases f6 = 0.6869 p error > 0.05 in 7 cases

I choose the interaction bathrooms:lat because has the lower p error and add a little more model_final_2

house_resid <- house_price %>%
  add_residuals(model_final_2) %>%
  select(-price)

coplot(resid ~ lat | bathrooms, data = house_resid)

calc.relimp(model_bath_view_lat_grade, type = "lmg", rela = TRUE)

Response variable: log(price) 
Total response variance: 0.2773966 
Analysis based on 21613 observations 

14 Regressors: 
Some regressors combined in groups: 
        Group  grade : grade3 grade4 grade5 grade6 grade7 grade8 grade9 grade10 grade11 grade12 grade13 

 Relative importance of 4 (groups of) regressors assessed: 
 grade bathrooms view lat 
 
Proportion of variance explained by model: 68.66%
Metrics are normalized to sum to 100% (rela=TRUE). 

Relative importance metrics: 

                 lmg
grade     0.43966938
bathrooms 0.21589254
view      0.09505446
lat       0.24938362

Average coefficients for different model sizes: 

             1group   2groups   3groups   4groups
bathrooms 0.3766719 0.2728513 0.1888339 0.1245107
view      0.2381620 0.1775130 0.1406023 0.1254952
lat       1.7073235 1.5941704 1.5201346 1.4767310
grade3    0.2177137 0.3022883 0.3886477 0.4764191
grade4    0.3139692 0.2939256 0.2684548 0.2375714
grade5    0.4597465 0.4301088 0.3935942 0.3502286
grade6    0.6802194 0.6318374 0.5751850 0.5103313
grade7    0.9729065 0.8941075 0.8028436 0.6992343
grade8    1.2724337 1.1635357 1.0384146 0.8972972
grade9    1.6236691 1.4914933 1.3406726 1.1715522
grade10   1.9390314 1.7785252 1.5966525 1.3939094
grade11   2.2676113 2.0700867 1.8474267 1.6003474
grade12   2.6454340 2.4080746 2.1419093 1.8479647
grade13   3.1642455 2.8611314 2.5210458 2.1452176

The most important is grade by 43% them bathrooms lat by 24 % bathroom by 21% and view by 9%